SPH Boundary Algorithm Based on Finite Difference Method and Its Application

doi:10.19596/j.cnki.1001-246x.8559

Abstract

Abstract:

Considering influence factors of virtual particle method in solving boundary problems, such as the increase of redundant calculation due to the large amount of particle search, we adopt SPH correction method in calculation domain, and use finite difference method at boundary, to realize a SPH boundary processing algorithm based on finite difference method. Taking the heat conduction problem as an example, the numerical simulation results are verified. It shows that as the proposed boundary treatment method is used to solve fixed and convective boundary heat conduction problems, numerical solution is in good agreement with analytical solution, and the numerical simulation process is reliable and effective. Advantages of the two algorithms complement each other, which provides a new idea for treatment of related boundary value problems.

Key words: kernel approximation, accuracy, finite different method, boundary algorithms, heat conduction

Jingxian PEI, Imin RAHMATJAN. SPH Boundary Algorithm Based on Finite Difference Method and Its Application[J]. Chinese Journal of Computational Physics, 2023, 40(3): 343-352.

Figures/Tables 8

Fig.1 Absolute error of second derivative calculation of unary functions

Fig.2 Absolute errors of second derivative calculation of binary functions (a) f1(x) = sin(πxy), (b) f2(x) =exp(-x2-y2), (c) f3(x) =(xy)3

Fig.3 Temperature curves of analytical and numerical solutions at 0.1 s, 0.2 s and 0.5 s for one-dimensional fixed boundary conditions

Fig.4 Temperature curves of analytical and numerical solutions for one-dimensional convectionboundary conditions at 0.1 s, 0.4 s and 0.6 s

Fig.5 Temperature curves of numerical solutions and analytical solutions for two-dimensional fixed boundary conditions at 0.2 s, 0.4 s and 0.6 s (a)x = 0.5, (b) y = 0.5

Fig.6 Temperature distributions of two-dimensional fixed boundary condition problem at t=1 s (a) analytical solution, (b) numerical solution

Fig.7 Temperature curves of numerical solutions and analytical solutions for two-dimensional convective boundary conditions at 0.2 s, 0.4 s and 0.6 s (a)x=0.5, (b)y=0.5

Fig.8 Temperature distributions of two-dimensional convective boundary problem at t=2s (a) analytical solution, (b) numerical solution

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